Lyotropic Liquid Crystals, Structures and Phase Transitions

Abstract

The most representative lyotropic liquid crystals are those formed by amphiphilic molecules, such as soaps, detergents and lipids, in presence of water. These molecules are able to build structures exhibiting a long range crystalline order, although they are disordered in a liquid-like manner at the local level. Their polymorphism is characterized by similar sequences of structures, whatever the details of the chemical structures of the molecules. These two characteristics, which will be discussed in the first part of the lecture, clearly show that the individual molecules can not be the building blocks of the structures and that the elements of structures are indeed the interfaces built by the molecules or, better, the symmetric films built by two facing interfaces. These structures can therefore be described as crystals of fluid films. In order to bring out a general basis for the understanding of this new class of crystals, we developed a model for studying periodic configurations of symmetric films, which will be presented in the second part of the lecture. Its basic hypothesis is the existence of a geometrical frustration resulting from the conflict between forces normal to the interfaces and forces parallel to the interfaces. We shall determine its possible solutions, as well as their sequence when its magnitude varies, following a geometrical approach similar to those developed for other cases of frustration in condensed matter physics.